Fractal Polyhedra, Flakes and Webs

I've started with these amazing Fractal Polyhedra obtained by Laurens Lapre's "LParser": pascal2 and koch1. See also Encyclopedia of Polyhedra by George W. Hart. Polyhedra Collection and VRMLArts by V.Bulatov
Look at Fractal Polyhedra with interactive Java 1.1 applet, if you didn't install a VRML plugin yet.
Stars

Kepler's (Stellated) Fractals

Hop David attracted my attention to Keplerian Fractals. He replaces every horn of a stellated (non-convex) polyhedron by small self-similar polyhedron. The picture shows that we can make it in two different ways (we will obtain a II-type (solid) fractal if we combine I-type ones).
Kepler's Dodecahedron Interactive Kepler's Octahedron is made of 4 Tetra Flakes. Hop David found out that it turns into a cube under iterations. He found "Cantor's Octahedron" beneath the cube's surface too.

Kepler's Stellated Dodecahedron I-type, II-type (solid)

Kepler's Great Stellated Dodecahedron I-type, II-type (solid). Polyhedra with many vertises are too complicated :(

Tetrahedron Web

Cantor's Webs

You will get 1D Fractal Web (may be Laces or Hedgehog :) if you start at "skeleton" of a Polyhedron. The skeleton is made of rays from the Polyhedron center to its verteses. Look at Interactive Tetrahedron Web and Pyramid Web.
1D Snowflake
Cubic Flake

Koch's Flakes

Interactive Tetra Flake (click it) is a simple 3D generalization of the 2D Snowflake. You take a equilateral triangle, shrink it 2 times and translate 6 copies (3 of them with rotation) to get "broken" equilateral triangle. Then repeat the process.

One more 3D Koch object - Interactive Cubic Flake.


3D Lab
updated 7 August 2000